Intersection numbers with Pixton's class and the noncommutative KdV hierarchy

Abstract

The Pixton class is a nonhomogeneous cohomology class on the moduli space of stable curves ${\overline{\mathcal{M}}}_{g,n}$, with nontrivial terms in degree $0,2,4,\dots ,2g$, whose top degree part coincides with the double ramification cycle. In this paper, we prove our conjecture from a previous work, claiming that the generating series of intersection numbers of the Pixton class with monomials in the psi-classes gives a solution of the noncommutative KdV hierarchy.

20 pages